Polysyllogism

A polysyllogism (also called multi-premise syllogism, sorites, climax, or gradatio) is a string of any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on. Each constituent syllogism is called a prosyllogism except the last, because the conclusion of the last syllogism is not a premise for another syllogism.

Example
An example for a polysyllogism is:


 * It is raining.
 * If we go out while it is raining we will get wet.
 * If we get wet, we will get cold.
 * Therefore, if we go out we will get cold.

Examination of the structure of the argument reveals the following sequence of constituent (pro)syllogisms:


 * It is raining.
 * If we go out while it is raining we will get wet.
 * Therefore, if we go out we will get wet.


 * If we go out we will get wet.
 * If we get wet, we will get cold.
 * Therefore, if we go out we will get cold.

Sorites
A sorites (plural: sorites) is a specific kind of polysyllogism in which the predicate of each proposition is the subject of the next premise. Example:


 * All lions are big cats.
 * All big cats are predators.
 * All predators are carnivores.
 * Therefore, all lions are carnivores.

The word sorites comes from σωρίτης, heaped up, from σωρός heap or pile. Thus a sorites is a heap of propositions chained together. A sorites polysyllogism should not be confused with the sorites paradox, a.k.a. the fallacy of the heap.

Lewis Carroll uses sorites in his book Symbolic Logic (1896). For example:


 * No experienced person is incompetent;
 * Jenkins is always blundering;
 * No competent person is always blundering.
 * Jenkins is inexperienced.

Carroll's example may be translated thus:


 * All experienced persons are competent persons.
 * No competent persons are blunderers.
 * Jenkins is a blunderer.
 * Jenkins is not an experienced person.